Alternate Forms of the One-Way ANOVA F, Kruskal-Wallis K, and Partitional Clustering B

Music City Center 

For ease of instruction, the one-way analysis of variance F statistic is rewritten in terms of pairwise differences in individual sample means instead of differences of individual sample means from the overall sample mean. For any pair of samples, the contribution to the F statistic is proportional to the product of the sample sizes multiplied by the square of the difference in the sample means. These comments also apply to the Kruskal-Wallis K, and the between sum of squares B statistic used in partitional clustering.

Teaching

Intuition 

Section on Statistics and Data Science Education